Reputation
13,543
Top tag
Next privilege 15,000 Rep.
Protect questions
Badges
1 69 147
Newest
 Nice Answer
Impact
~114k people reached

Jun
29
accepted Fourier transform of squared exponential integral $\operatorname{Ei}^2(-|x|)$
Jun
26
revised Reducing multi-variable functions to a composition of 1- or 2-variable functions
added 478 characters in body
Jun
26
awarded  Nice Answer
Jun
26
asked Reducing multi-variable functions to a composition of 1- or 2-variable functions
Jun
25
comment Simplify $7\arctan^2\varphi+2\arctan^2\varphi^3-\arctan^2\varphi^5$
For example, $\displaystyle\arctan\varphi^{11}=\frac{5\pi}{4}+\frac{1}{2}\,\arctan{2}-\arctan‌​{5}-\arctan{34}.$
Jun
25
revised Simplify $7\arctan^2\varphi+2\arctan^2\varphi^3-\arctan^2\varphi^5$
\phi -> \varphi for consistency
Jun
25
comment Simplify $7\arctan^2\varphi+2\arctan^2\varphi^3-\arctan^2\varphi^5$
@JackD'Aurizio That was a very nice problem! It looks like higher integer powers of $\varphi$ cannot be expressed as rational linear combination of $\pi$ and $\arctan2$, but some (not all) of them can if we add more $\arctan n$ terms, and for some a zero linear combination with several $\arctan\varphi^n$ terms exists. It would be great to analyze this behavior deeper.
Jun
25
answered Simplify $7\arctan^2\varphi+2\arctan^2\varphi^3-\arctan^2\varphi^5$
Jun
24
awarded  Nice Answer
Jun
24
comment How to compute $\int_0^\infty \frac{1}{(1+x^{\varphi})^{\varphi}}\,dx$?
By the way, the antiderivative is elementary: ${\large\int}\frac{1}{(1+x^{\varphi})^{\varphi}}\,dx=\frac{x}{\left(1+x^{\varphi‌​}\right)^{1/{\varphi}}}+C$ that can be verified by direct differentiation and simplification using the identity $1/\varphi=\varphi-1$.
Jun
16
comment Integral ${\large\int}_0^\infty\frac{dx}{\sqrt[4]{7+\cosh x}}$
@Lucian Yes, there was a typo in the closed form I gave. It should be $3$, not $2$ in the denominator. I fixed it. Thanks! Sorry for the confusion...
Jun
16
revised Integral ${\large\int}_0^\infty\frac{dx}{\sqrt[4]{7+\cosh x}}$
fix typo in closed form
Jun
15
awarded  Nice Question
Jun
15
revised Integral ${\large\int}_0^\infty\frac{dx}{\sqrt[4]{7+\cosh x}}$
added 105 characters in body
Jun
15
comment Integral ${\large\int}_0^\infty\frac{dx}{\sqrt[4]{7+\cosh x}}$
The intergral has an equivalent form $\displaystyle\sqrt[4]{2}\,\int_0^\infty\frac{dx}{\sqrt[4]{16 + 64 x + 97 x^2 + 67 x^3 + 19 x^4 + x^5}}$.
Jun
15
asked Integral ${\large\int}_0^\infty\frac{dx}{\sqrt[4]{7+\cosh x}}$
Jun
15
accepted Closed form for ${\large\int}_0^\pi\frac{x\,\cos\frac x3}{\sqrt[3]{\sin x}}dx$
Jun
15
revised Closed form for ${\large\int}_0^\pi\frac{x\,\cos\frac x3}{\sqrt[3]{\sin x}}dx$
edited body
Jun
14
asked Closed form for ${\large\int}_0^\pi\frac{x\,\cos\frac x3}{\sqrt[3]{\sin x}}dx$
Jun
12
comment The log integrals $\int_{0}^{1/2} \frac{\log(1+2x) \log(x)}{1+x} \, dx $ and $ \int_{0}^{1/2} \frac{\log(1+2x) \log(1-x)}{1+x} \, dx$
@RandomVariable Yes, please.